Pharmaceutical Calculations PHT 210

Dr. Musaed Alkholief

Office: AA 119

Email: malkholief@ksu.edu.sa

Office hours: every day except Monday

From 11 am – 12 pm

By appointment only1

Syllabus

Reference:

• Pharmaceutical Calculations 13th and 14th editions. Howard C. Ansel

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Electrolytes

19/10/2015

6/1/1437

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Introduction

• Mixtures:

- Two or more different substances that are mixed with each other.

- Can be either heterogeneous or homogenous.

alterecofoods.com

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Solutions:

• Homogenous mixtures composed of solute and solvent.

- Solute: a substance that gets dissolved.

- Solvent: a substance that do the dissolving.

• Water is the most common solvent in nature

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• Depending on the chemistry of the solute, substances can dissolve in water forming either electrolytes and non electrolytes.

• Electrolytes:

- Substances that dissociate partly or completely in water yielding ions.

- A solution that has ions can conduct electricity.

• Non Electrolytes:

- Substances that dissolve in water without dissociating, rather they remain as molecules. (no ions, no conductivity)

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Electrolytes:

• Dissociate into ions, either +ve (cathode) or –ve (anode).

• Depending on the degree of dissociation, they can be either:

1- Strong electrolytes:

- Completely ionized in water.

- Strong conductor.

- Example:

NaCl (s) Na+ (aq) + Cl- (aq)

H2O

2- weak electrolytes:

- Partly ionized in water

- Weak conductor.

- Example:

CH3COOH(l) H+ (aq) + CH3COO-

(aq)

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In our bodies..

• Cations present include: Na+, K+, Ca++ and Mg++ and the anions Cl-, HCO3-, HPO4

-- andSO4

--.

• These electrolytes play important role in maintaining acid-base balance in the body.

• In addition, they control body water volume and regulate body metabolism.

As a dosage forms:

- Pharmaceutical dosage forms containing electrolytes are used to treat electrolytedisturbance of body fluids in the form of I.V infusion, tablets, capsules, oralrehydrating solution (ORS) .

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Electrolyte concentration can be expressed as:

• Percent solutions (w%) (w/v)

• Millimoles (mmol) and Micromoles (µmol)

• Milliequivalents (mEq)

• Milliosmoles (mOsmol)

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1- Percent solutions

• Ratio of solute to solvent expressed as percentage (w%)

= weight in GRAMS/ 100 ml volume of a solution (w/v)

• Commonly seen in IV bags and medical solutions.

• Example

- 5% Dextrose 5 g dextrose in 100 ml solution

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2- Millimoles and Micromoles

• Mole= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)

𝑀𝑊

• Millimoles = 10-3 of a mole

• Micromoles= 10-6 of a mole

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3- Milliequivalents

• It is concerned with the total number of ions in a solution (related to valency).

• It is a measurement of the chemical activity of an electrolyte.

mEq= 𝑚𝑔

𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑤𝑒𝑖𝑔ℎ𝑡

• Equivalent weight:

- The amount of a substance that will either:

supply or react with one mole of hydrogen ions (H+) in an acid-base reaction; or

supply or react with one mole of electrons in a redox reaction.

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Equivalent weight= 𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑙𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑤𝑒𝑖𝑔ℎ𝑡

𝑣𝑎𝑙𝑒𝑛𝑐𝑒

Therefore,

mEq= 𝑚𝑔 𝑥 𝑣𝑎𝑙𝑒𝑛𝑐𝑒

𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑎𝑙 𝑤𝑒𝑖𝑔ℎ𝑡

And

mg= 𝑚𝐸𝑞 𝑥 𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑤𝑒𝑖𝑔ℎ𝑡

𝑣𝑎𝑙𝑒𝑛𝑐𝑒

• You can always represent mEq and mg as mEq/ml and mg/ml

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4- Osmolarity

• Takes into account the number of particles of solute in the solution.

• The unit of osmotic concentration is the milliosmole (mOsmol).

• For electrolytes (as NaCl) in which dissociation occurs:

1 mmole of NaCl = 2 mOsmol (Na+ + Cl-)

1 mmole of CaCl2 = 3 mOsmol (Ca++ + 2Cl-)

• N.B.: For any atom in solution, No. of species= 1

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mOsmol= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)

𝑀𝑊X number of species X 1000

= moles X number of species X 1000

Can be represented as mOsmol/L and gram/L

mOsmol/L = 𝑤𝑒𝑖𝑔ℎ𝑡 (

𝑔

𝐿)

𝑀𝑊X number of species X 1000

• For non-electrolytes (as dextrose) in which no dissociation occurs, mmole=mOsmol.

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Percent solutions:

= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)

100𝑚𝐿 𝑜𝑓 𝑎 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

Millimole:

Mole= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)

𝑀𝑊

millimole= mole/1000 micromole= mole/1000000

Milliequivlent:

mEq= 𝑚𝑔 𝑥 𝑣𝑎𝑙𝑒𝑛𝑐𝑒

𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑎𝑙 𝑤𝑒𝑖𝑔ℎ𝑡

mg= 𝑚𝐸𝑞 𝑥 𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑤𝑒𝑖𝑔ℎ𝑡

𝑣𝑎𝑙𝑒𝑛𝑐𝑒

Milliosmole:

mOsmol= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)

𝑀𝑊X number

of species X 1000

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1- What is the concentration in (mg/ml) of a solution containing 2 mEq ofpotassium chloride per milliliter?

M.W. of KCl = 74.5

mg/ml= 𝑚𝐸𝑞/𝑚𝑙 𝑥 𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑤𝑒𝑖𝑔ℎ𝑡

𝑣𝑎𝑙𝑒𝑛𝑐𝑒

= 2 ∗ 74.5

1= 149 mg/ml

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2- A solution containing 10 mg/100mL of K+1. Express the solution in terms of milliequivalents per liter (mEq/L).

Atomic weight of K+1 = 39

mEq/ml= 𝑚𝑔/𝑚𝑙 𝑥 𝑣𝑎𝑙𝑒𝑛𝑐𝑒

𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑎𝑙 𝑤𝑒𝑖𝑔ℎ𝑡

= 10𝑚𝑔/100𝑚𝑙 𝑥 1

39

= 0.2564 mEq/100 ml

= 2.56 mEq/L

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3- What is the percent (w/v) of a solution containing 100 mEq of Ammoniumchloride per Liter?

M.W. of NH4Cl = 53.5

mg/L= 𝑚𝐸𝑞/𝐿 𝑥 𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑤𝑒𝑖𝑔ℎ𝑡

𝑣𝑎𝑙𝑒𝑛𝑐𝑒

= 100𝑚𝐸𝑞/𝐿 𝑥 53.5

1

= 5350 mg/L

= 5.35 g/L

= 0.535 g/100 ml or 0.535 g%

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4- A solution containing 10 mg/100mL of Ca++. Express the solution in terms of milliequivalents per liter (mEq/L).

Atomic weight of Ca++ = 40

mEq/ml= 𝑚𝑔/𝑚𝑙 𝑥 𝑣𝑎𝑙𝑒𝑛𝑐𝑒

𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑎𝑙 𝑤𝑒𝑖𝑔ℎ𝑡

= 10

𝑚𝑔

100𝑚𝑙∗ 2

40

= 0.5 mEq/100 ml

= 5 mEq/L

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5- Magnesium ions level in the blood plasma is 2.5mEq/L. Express theconcentration in terms of milligrams.

Atomic weight of Mg++ = 24

mg/L= 𝑚𝐸𝑞/𝐿 𝑥 𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑤𝑒𝑖𝑔ℎ𝑡

𝑣𝑎𝑙𝑒𝑛𝑐𝑒

= 2.5 𝑚𝐸𝑞/𝐿 𝑥 24

2

= 30 mg/L

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6- A person is to receive 2mEq of sodium chloride per kilogram of body weight. Ifthe person weighs 60 kg, how many milliliters of 0.9 % sodium chloride sterilesolution should be administered?

Molecular weight of NaCl = 58.5

mg= 𝑚𝐸𝑞 𝑥 𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑤𝑒𝑖𝑔ℎ𝑡

𝑣𝑎𝑙𝑒𝑛𝑐𝑒

Total mEq required= 2 x 60= 120 mEq

mg= 120𝑚𝐸𝑞 ∗58.5

1= 7020 mg

0.9 g --------> 100 ml

7.020 g -----> x ml

NaCl needed= 780 ml26

7- A patient is given 125 mg of phenytoin sodium (m.w. 274) three times a day. How many milliequivalents of sodium are represented in daily dose?

mEq= 𝑚𝑔 𝑥 𝑣𝑎𝑙𝑒𝑛𝑐𝑒

𝑎𝑡𝑜𝑚𝑖𝑐,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟,𝑜𝑟 𝑓𝑜𝑟𝑚𝑢𝑎𝑙 𝑤𝑒𝑖𝑔ℎ𝑡

125 mg three times a day = 375 mg

= 375 𝑥 1

274

= 1.37 mEq27

8- Ringer’s solution contains 0. 86% of NaCl, 0.035 % of KCl and 0.033% CaCl2.How many mEq of each chloride are contained in 1 L of the injection.

m.w.: of NaCl= 58.5, KCl= 74.5 and CaCl2 = 111

A- NaCl: 0.86%= 0.86 g/100 mL= 8.6 g/ L= 8600 mg/L

mEq of NaCl = (wt x valence)/ m.w.

= (8600 x 1)/ 58.5 = 147 mEq

B- KCl: 0.03%= 0.03 g/100 mL= 0.3 g/ L= 300 mg/L

mEq of KCl = (wt x valence)/ m.w.

= (300 x 1)/ 74.5 = 4.03 mEq

C- CaCl2: 0.033%= 0.033 g/100 mL= 0.33 g/ L= 330 mg/L

mEq of CaCl2 = (wt x valence)/ m.w.

= (330 x 2)/ 111 = 5.95 mEq 28

9- How many Millimoles of dibasic sodium phosphate in 100 g of substance?

M.W. of dibasic sodium phosphate is 138.

Number of moles= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)

𝑀𝑊= 100 𝑔

138= 0.725 moles = 725 mmoles

10- How many milligrams would 3 mmoles of dibasic sodium phosphate weigh?

M.W. of dibasic sodium phosphate is 138.

Number of moles= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)

𝑀𝑊 weight (g) = moles * MW

= 0.003 * 138 = 0.414 g = 414 mg

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11- Convert Tobramycin blood plasma levels of 0.5 μg/mL and 2 μg/mLinto μmoles.

M.W. of Tobramycin is 467.5.

Mole= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)

𝑀𝑊

Millimole= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑚𝑔)

𝑀𝑊

Micromole = 𝑤𝑒𝑖𝑔ℎ𝑡 (µ𝑔)

𝑀𝑊

= 0.5

467.5= 1.07 x 10-3 μmole

And, 2

467.5= 4.27 x10-3 μmole

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12- What is the osmolarity of 0.9%w/v NaCl injection?

mOsmol= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)

𝑀𝑊X number of species X 1000

0.9% w/v= 0.9 g/ 100 mL = 9 g/L

mOsmol= 9

58.5X 2 X 1000

= 308 mOsmol

= 0.308 Osmol

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13- A solution contains 156 mg of K+ ions per 100 mL. How many mOsmoles are represented in a liter of the solution? Atomic weight of K+ =39

mOsmol/L = No. of moles x No. of species x 1000

156 mg/100 mL = 0.156 g/ 100 mL= 1.56 g/L

Number of moles= weight/ atomic Wt= 1.56/39= 0.04

mOsmol/L = 0.04 x 1 x 1000= 40 mOsmol/L

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14- A solution contains 10 mg% of Ca++ ions. How many milliosmoles arerepresented in one liter of the solution?

Atomic weigh of Ca++ = 40

mOsmol/L = No. of moles x No. of species x 1000

10 mg%= 10 mg/100mL = 100 mg/L= 0.1 g/L

Number of moles= weight/ atomic wt= 0.1/40= 0.0025

mOsmol/L = 0.0025 x 1 x 1000= 2.5 mOsmol/L

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15- A parenteral solution contains 5% dextrose. How many mOsmoles per literare represented by this concentration?

M.W. of dextrose = 180

mOsmol/L= 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔/𝐿)

𝑀𝑊X number of species X 1000

5% = 5 g/100 mL = 50 g/ L

Dextrose is non-electrolye, so, number of species = 1

mOsmol/L = 50

180X 1 X 1000

= 278 mOsmol/L

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